
First, we build groups at random, which serves as a null model that helps to discover unexpected behaviors.

Second, groups are dictated by proximity in geometric network maps, allowing to explore the role of homophily in enhancing or hindering consensus. These similarity groups are formed by dividing the similarity space in angular sectors with \(r\)  consecutive nodes (see Fig. REF ). This is a coarse-graining procedure which is at the core of the geometric renormalization group for networks introduced in [1]}. For consistency, we always start making the groups from the node with \(\theta _{\mathrm {min}}\)  but this is an arbitrary choice due to the rotational symmetry of the circle.

Finally, groups are based on geometric communities [2]}, which tests the influence of the network's intrinsic modular organization into the opinion formation process. Geometric communities are essentially similarity groups of different sizes partitioned to maximize modularity. Further details regarding community-based groups are discussed in Methods.

